Mathematics: Tips for Solving Simple Equations Problems in Competitive Exams

Tips for Solving Simple Equations Problems 

An equation is a statement where the two sides are equal. In other words, equations are combinations of one or more letters/numbers lying on each side of an "equal to" (=) sign. They are valid or true for certain values of the letters only. The letters in the equation are called the unknowns.

For Example: What number multiplied by 6 gives a product of 18 ?

You may calculate with the help of tables and find out the answer as 3. (you can recall the table of 6 or you can divide 18 by 6 to find out the answer). However, there is another method of finding out that number.

Suppose the number is X.

6 x X = 18 (given in the question)

6X = 18 => X = 18/6

                    X = 3.

Equation are Classified into:

• Polynomial Equations: If f(x) is real or complex polynomial, then f(x) =0 is known as a polynomial equation. 

• Linear Equations in One Variable: These are first degree equations in one unknown. An equation of the form ax + b = 0 where a, b subset of R and a not equal to zero and x is the variable, is called a linear equation in one variable. The value of x which satisfies the given equation, is called its solution.

• Linear Equation in Two Variables: These are first degree equation in two unknowns. An equation of the form ax + by + c = 0, where a, b, c subset of R and a not equal to 0, b not equal to 0 and x, y are variables is called linear equation in two variables. Any pair of values of x and y which satisfy the equation ax + by + c = 0, is called its solution.

• Quadratic Equation: These are second degree equations in one unknown. An equation of the form ax² + bx + c = 0, where a, b, c subset of R and a not equal to 0 is called quadratic equation. Like a first degree equation in x has one value of x satisfying the equation, a quadratic equation in x will have two values of x that satisfy the equation. The value of x that satisfy the equation are called the root of the equation. These roots may be real or imaginary.

Important Points to Remember:

• You can add to or subtract any number or quantity from each side of an equation without upsetting the balance.
• You can multiply or divide both sides of an equation by the same number without upsetting the balance.
• You can transfer any number or quantity from one side of the equation to the other if you change its sign ( + to - ) or ( - to +) when you do so.

Sample Problems:

1) What is the number which, when added to 6, become 15 ?

Sol:-

    You may just count and calculate and find out the answer as 9 (15 - 6 = 9).

     Better you solve the question with the help of an equation.

              Suppose the number is X.

There fore X + 6 = 15.

        Now X = 15 - 6.  = 9

                X = 9.

 

2) Find Y, if ½(3Y = 1) - 1/3(5Y + 2) = Y -1

Sol:-

          ½(3Y + 1) - 1/3(5Y + 2) = Y-1

=> (9Y + 3) - (10Y + 4) = 6Y - 6

=> -Y -1 = 6Y - 6

=> 7Y = 5

=> Y = 5/7